Precise Rates in the Law of the Iterated Logarithm under Dependence Assumptions  

作　　者：Wel Dong LIU Zheng Yan LIN 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第1期59-74,共16页数学学报（英文版）

基　　金：National Natural Science Foundation of China (No.10571159)

摘　　要：Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2（log2{X}）^2〈∞and φ（n）=O（1/log n）^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O（√n/（log2n）^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP（｜Sn｜≥ε√ESn^2log2n＋an）=√2.The results of Gut and Spataru （2000） are special cases of ours.Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2（log2{X}）^2〈∞and φ（n）=O（1/log n）^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O（√n/（log2n）^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP（｜Sn｜≥ε√ESn^2log2n＋an）=√2.The results of Gut and Spataru （2000） are special cases of ours.

关 键 词：law of the iterated logarithm mixing sequences strong approximation 

分 类 号：O17[理学—数学]